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Evaluation of scenario reduction algorithms with nested distance

Author

Listed:
  • Markéta Horejšová

    (Charles University)

  • Sebastiano Vitali

    (Charles University
    University of Bergamo)

  • Miloš Kopa

    (Charles University)

  • Vittorio Moriggia

    (University of Bergamo)

Abstract

Multistage stochastic optimization is used to solve many real-life problems where decisions are taken at multiple times. Such problems need the representation of stochastic processes, which are usually approximated by scenario trees. In this article, we implement seven scenario reduction algorithms: three based on random extraction, named Random, and four based on specific distance measures, named Distance-based. Three of the latter are well known in literature while the fourth is a new approach, namely nodal clustering. We compare all the algorithms in terms of computational cost and information cost. The computational cost is measured by the time needed for the reduction, while the information cost is measured by the nested distance between the original and the reduced tree. Moreover, we also formulate and solve a multistage stochastic portfolio selection problem to measure the distance between the optimal solutions and between the optimal objective values of the original and the reduced tree.

Suggested Citation

  • Markéta Horejšová & Sebastiano Vitali & Miloš Kopa & Vittorio Moriggia, 2020. "Evaluation of scenario reduction algorithms with nested distance," Computational Management Science, Springer, vol. 17(2), pages 241-275, June.
    • Handle: RePEc:spr:comgts:v:17:y:2020:i:2:d:10.1007_s10287-020-00375-4
    DOI: 10.1007/s10287-020-00375-4
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    References listed on IDEAS

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    1. Anna Timonina, 2015. "Multi-stage stochastic optimization: the distance between stochastic scenario processes," Computational Management Science, Springer, vol. 12(1), pages 171-195, January.
    2. Miloš Kopa & Vittorio Moriggia & Sebastiano Vitali, 2018. "Individual optimal pension allocation under stochastic dominance constraints," Annals of Operations Research, Springer, vol. 260(1), pages 255-291, January.
    3. Raimund Kovacevic & Alois Pichler, 2015. "Tree approximation for discrete time stochastic processes: a process distance approach," Annals of Operations Research, Springer, vol. 235(1), pages 395-421, December.
    4. Sebastiano Vitali & Vittorio Moriggia & Miloš Kopa, 2017. "Optimal pension fund composition for an Italian private pension plan sponsor," Computational Management Science, Springer, vol. 14(1), pages 135-160, January.
    5. Mandelli, Diego & Yilmaz, Alper & Aldemir, Tunc & Metzroth, Kyle & Denning, Richard, 2013. "Scenario clustering and dynamic probabilistic risk assessment," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 146-160.
    6. Soňa Kilianová & Georg Pflug, 2009. "Optimal pension fund management under multi-period risk minimization," Annals of Operations Research, Springer, vol. 166(1), pages 261-270, February.
    7. Moriggia, Vittorio & Kopa, Miloš & Vitali, Sebastiano, 2019. "Pension fund management with hedging derivatives, stochastic dominance and nodal contamination," Omega, Elsevier, vol. 87(C), pages 127-141.
    8. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    9. Holger Heitsch & Werner Römisch, 2009. "Scenario tree reduction for multistage stochastic programs," Computational Management Science, Springer, vol. 6(2), pages 117-133, May.
    10. Patrizia Beraldi & Maria Bruni, 2014. "A clustering approach for scenario tree reduction: an application to a stochastic programming portfolio optimization problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 934-949, October.
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    3. Alkhaleel, Basem A. & Liao, Haitao & Sullivan, Kelly M., 2022. "Risk and resilience-based optimal post-disruption restoration for critical infrastructures under uncertainty," European Journal of Operational Research, Elsevier, vol. 296(1), pages 174-202.

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